Telematics systems are used in vehicles to determine the position and speed of a vehicle over time. Typically a global positioning system (GPS) is mounted on a vehicle to provide information about the location of the vehicle relative to geo-synchronous satellites and from this the speed and acceleration of the vehicle can be obtained from readings obtained over time. To provide more reliable acceleration information, the GPS is often used in combination with an accelerometer also mounted on the vehicle. The orientation of the accelerometer relative to the vehicle is unknown and must be derived using information from the GPS and the accelerometer. Prior art methods for calibrating the orientation of the accelerometer relative to the GPS can involve acquisition and storage of large amounts of data, so compromising processing speed unless expensive data processors are used. Other methods involve determining the orientation of the accelerometer while the vehicle is stationary which can introduce a bias and result in an inaccurate calibration, so giving incorrect information about the vehicle's speed and acceleration.